Integer and constraint programming approaches for providing optimality to the bandwidth multicoloring problem

¹ Instituto de Computação (IComp/UFAM), Universidade Federal do Amazonas, Manaus, Brazil
² PESC/COPPE, Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro – RJ, Brazil
³ Centre d’Enseignement et de Recherche en Informatique, Université d’Avignon et des Pays de Vaucluse, Avignon, France

^* Corresponding author: bruno.dias@icomp.ufam.edu.br

Received: 31 December 2018
Accepted: 17 June 2020

Abstract

In this paper, constraint and integer programming techniques are applied to solving bandwidth coloring problems, in the sense of proving optimality or finding better feasible solutions for benchmark instances from the literature. The Bandwidth Coloring Problem (BCP) is a generalization of the classic vertex coloring problem (VCP), where, given a graph, its vertices must be colored such that not only adjacent ones do not share the same color, but also their colors must be separated by a minimum given value. BCP is further generalized to the Bandwidth Multicoloring Problem (BMCP), where each vertex can receive more than one different color, also subject to separation constraints. BMCP is used to model the Minimum Span Channel Assignment Problem (MS-CAP), which arises in the planning of telecommunication networks. Research on algorithmic strategies to solve these problems focus mainly on heuristic approaches and the performance of such methods is tested on artificial and real scenarios benchmarks, such as GEOM, Philadelphia and Helsinki sets. We achieve optimal solutions or provide better upper bounds for these well-known instances, We also compare the effects of multicoloring demands on the performance of each exact solution approach, based on empirical analysis.